The unified method for the three-wave equation on the half-line

We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the three-wave equation: $p_{ij,t}-\frac{b_i-b_j}{a_i-a_j}p_{ij,x}+\sum_k(\frac{b_k-b_j}{a_k-a_j}-\frac{b_i-b_k}{a_i-a_k})p_{ik}p_{kj}=0,\quad i,j,k=1,2,3.$ on the half-line.

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